# Normal Distribution

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## Normal Distribution

The well known bell shaped curve. According to the Central Limit Theorem, the probability density function of a large number of independent, identically distributed random numbers will approach the normal distribution. In the fractal family of distributions, the normal distribution only exists when alpha equals 2, or the Hurst exponent equals 0.50. Thus, the normal distribution is a special case which in time series analysis is quite rare. See: Alpha, Central Limit Theorem, Fractal Distribution.

## Bell Curve

A curve on a chart in which most data points cluster around the median and become less frequent the farther they fall to either side of the median. When plotted on a chart, a bell curve looks roughly like a bell.
References in periodicals archive ?
To demonstrate that the data are approximately normally distributed, Figs, 1a and lb display the skew and kurtosis (shown as differences from 3, the kurtosis of a normal distribution) of 36 daily values along the tracks of each polar party.
The experimental errors are assumed to be independently and normally distributed. Estimation of parameters and statistical inferences can be possible if and only if this assumption is valid.
If we assume our process is normally distributed, and measure Pp = 2.0 (Six-Sigma process), this means we are predicting extremely low ppm levels of defects: less than 0.002 ppm (3.4 ppm with the irritating 1.5 shift).
Shapiro-Wilk univariate normality tests indicated that total hours of sleep were not normally distributed at the time of the pretests (Table 1).
Thus, we present the calculation process of paired t-test and independent t-test in the data analysis, respectively, under the assumption that both samples come from normally distributed populations with unknown but equal variances.
Comparisons between normally distributed data were done using Student's t-test; for data not normally distributed we used the Wilcoxon Mann-Whitney U-test.
At 0.01 significance level of alpha, the critical values of chi square distribution with 2 degrees of freedom must be less than 9.21 under Jarque-Bera test for a normally distributed data.
One of them, which have different time-sequence phases and multiple attribute indexes of normally distributed stochastic variables, like street traffic flow, shopping centre popularity at different times, or the customer waiting times, is referred to as dynamic stochastic multiattribute decisionmaking problems.
An unpaired two-tailed i-test based on ranks (Mann-Whitney) was used to compare differences between two groups for data that were not normally distributed and a two-tailed unpaired Student's i-test was used for normally distributed data.
The simple assumption that the measurement errors are normally distributed does not lead to a statistically normal distribution, but to a "Cauchy," "ratio," or "Lorentzian" distribution, which cannot be parameterized like a normal distribution since it contains infinite values when the denominator goes to zero [7].
The latitude variations in the zero meridian are simulated by the same time series of polar motion plus a model of normally distributed random errors N(0, 0.1 as), based on Forsythe, Malcolm and Moler algorithm (Forsythe et al., 1977).

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